Terminating network for filters



Oct. 13,1925- 1,557,229

0. J. ZOBEL TBRIINATING NETWORK FOR FILTERS Filed April 30 1920 16Sheets-Sheet 1 V !N V EN TOR.

O. JZaeZ Oct. 13, 1925. 1,557,229

0. J. ZOBEL TERMINATING NETWORK FOR FILTERS Filed April 30, 1929 6Sheets-Sheet 2 i I Z125 4.? 195' g A 5 L 2 7; 5/ W 'WWW (Jul) 1:5 34 x52 52 Z 4 c WW\N I 2 4; 7 :2 7 [Z 32 z; INVENTOIL [Md BY Wi A TTORNEY 03L13, O. J. ZOBEL TERMINATING NETWORK FOR FILTERS Filefi April 30 1920 6Sheets-Sheet 4 flM-Jzwbr@az2wle1z 'Z i/pay noon nun nun 4 2 2 [fix/Z T I4)? .JwC 2c T o 0 I non nun 5;, Z T .56 f 2k 1 c nun nun nun 3 o, 0 c c.15

T T T 4 4c is T M 1? W 4% v 0 INVENTOR. QJZahJ 7%; ATTORNEY O. J. ZOBELTBRIINATING NETWORK FOR FILTERS Filed Apr 1 1920 6 Sheets-Sheet 6JW-Jer'ar uni) @var l1 g L Q 4/ Q o 0 o I 1 IN V ENYUR.

O JZae Q ATTORNEY Patented Oct. 13, 1925.

UNITED STATES PATENT OFFICE.

OTTO J. mBEL, OF MAPLEWOOD. NEW JERSEY, ASSIGNOR TO AMERICAN TELEPHONEAND TELEGRAPH COMPANY. A CORPORATION OF NEW YORK.

TERMINATING NETWORK FOR FILTERS.

Application filed April 30, 1920. Serial No. 377,964.

T all whom it may concern:

Be it known that I. O'rro J. ZOBEL, residing at Maplewood. in the countyof Essex and State of New Jersey. have invented certain Improvements inTerminating Networks for Filters. of which the following is aspecification.

This invention relates to selective circuits of the type known as wavefilters, and more articularly to terminating arrangements or suchfilters.

ave filters. as heretofore known in the art. consist of networks havinga plurality of similar periodic sections. each section ineluding aseries and a shunt impedance element. lVave'filters of this general typeand their properties have been described in U. S. patents to George A.Campbell Nos. 1.227.113 and 1.227.114 issued May 22. 1917. l'n generalwhen a wave filter of the type above referred to is connected to a linewhose impedance is practically a constant resistance. large impedanceirregularities are introduced between the wave filter and the line inthe range of frequencies to be transmitted. since the characteristicimpedance of the filter for any termination varies greatly withfrequency. These impedance irregularities at the frequencies to betransmitted are objectionable. not only from the standpoint. of maximumenergy transferred from the line to the wave filter, but also from thestandpoint of repeater balance.

The wave filters forming the subject mat ter of this invention have asingly periodic structure consisting of a plurality of sections. asindicated in Fig. 2. each section comprising a series impedance elemente and a shunt impedance element 2 These impedance elements arereactances. that is, they are made up of inductances and capacities ina. manner more fully hereafter described. While the discussion of theseWave filters is primarily on the basis that the elements arenon-dissipative in character, the inevitable introduction of dissipationwill not materially alter the designs obtained. In order to minimize thetransmission losses in the wave filter. there should be provided aslarge time constants for the inductances and capacities as ispracticable in each specific case.

The computation for a filter on the assumed basis that its reactancesare non-dissipatire is justified both by theoretical investigations andby practical tests. It is well known that the resistance of a coil or acondenser can be made very small compared to its inductive reactance orcapacity reactance, and therefore the performance of such a coil orcondenser may be computed approximately with entire neglect of suchslight resistance.

Vhen the magnitudes of the inductances and capacities have been obtainedin this basis and the types of coils and condensers giving thesemagnitudes have been decided upon. the corresponding amounts ofresistance necessarily introduced are then accurately talren account ofin practice when computing the current losses thru the wavefilter Theeffect of this dissipation is principally to cause small allowablecurrent losses within the bands of free transmission.

T have discovered that certain types of these filters have a propertywhich was not pointed out by Campbell in his patents, and one which. inpractice. is of considerable importance. namely that the product of theseries and shunt impedances of any section is equal to the square of avconstant which constant may, by proper design of the filter. be madeequal to the resistance of the line with which the filter is associated.Filters having this property are known as constant 7c filters.

One of the objects of the present invention is to provide suchtermination for a constant A wave filter. that the impedance of thefilter, over raotically the entire range of transmitted frequencies. maybe made practically a constant resistance equal to Z. Z being preferablyequal to the resist ance of the line with which the filter is to beassociated. Another object of the inven tion is to provide such aterminating arrangement for a filter that the filter Will be givenpractically infinite attenuation just outside the transmitting range,thereb increasing the sharpness of the cutoff.

ther

and further objects of the invention will more fully a pear hereinafter.

There are in general two types of terminations. In one type, known asthe m-series termination. where or may have any value from to unity, thenetwork terminates in a series element whose impedance is Ll times theimpedance of a full series element. that is, if a, be taken to designatethe im edanee of the series elen'ient, the terminating element will havean impedance .122 In the other type of termination. known as thetF-Shllllt termination, the network terminates in a shunt element whoseadmittance is n: times the admittance of a full shunt element 2:; thatis, it has an impedance I have discovered that a part of the ac seriescharacteristic admittance of any 'sin ly periodic recurrent network,whether ductance will be substantially over most of the transmittingrange. Hence. for types of filters in which Z' is constant, the totalimpedance in the transmitting range will. under these conditions, withthe annulling element provided. be practically equal to k=constant.

I have also found that a part of the .r-shunt characteristic impedancema y be. annulled by an addition of a series annulling element when .ris reater than .5. For a wave filter this annulled part is, in thetransmitting range, the reactance. There remains in this range aresistance. R variable with frequency. This resistance is substantiallyequal to I." over most of the transmitting range where .c has a value inthe neighborhood of .8. Therefore, if k is constant, the total impedancein the transmitting range will, if the annulling element be provided.again be practically equal to k=constant.

The invention will now be more fully understood from the followingdescription, when read in connection with the accompanying drawings. inwhich I Fig. 1 shows a number of curves illustrating the characteristicsof certain filter terminations.

Fig. 2 is a simplified diagram of a wave filter having an .1 seriestermination.

Fig. 3 is a diagram of a shunt annulling element for use in connectionwith the filter in Fig. 2.

Fig. 4 is a simplified diagram of a filter having an av shunttermination.

Fig. 5 is a diagram showing a series annulling element for use inconnection with the filter in Fig. 4.

Fig. 6 is a simplified diagram of a filter terminating in mid-series.

Figs. 7 and 8 are diagrams of terminating arrangements or annullingelements for the filter in Fig. 6.

Fi 9 is a simplified diagram of a filter ternnnating in mid-shunt.

Figs. 10 and 11 are diagrams of annulling elements for use in connectionwith the filter of Fig. 9.

Fig. 1-2 is a diagram of a low pass filter terminating in mid-series.

Figs. 13 and 14 illustrate the corresponding annulling elements.

Fig. 1:) is a diagram of a low pass filter terminating in mid-shunt.

Figs. 16 and 17 illustrate the corresponding annulling elements.

Fig. IR is a diagram of a high pass filter terminating in mid-series.

Figs. it) and .20 illustrate the corresponding annulling elements.

Fig. 21 is a diagram of a high pass filter terminating in mid-shunt.

Figs. and 23 illustrate the corresponding annulling elements.

Fig. 21- is a diagram of a band filter terminating in mid-series.

Figs. 25 and 26 illustrate the corresponding annulling elements.

Fig. 27 illustrates a band filter having a mid-shunt termination. theproper annulling tlfilll ltis' being illustrated in Figs. 98 and Q9.

description will now be given of two methods of terminating a constant1' wave filter. so that the resulting corre ted impedance issubstantially a constant resistance l throughout the transmitting rangeof the wave filter. For the best correction one method terminates thewave filte in .809- series (that is. in a series element whose impedanceis .809 times that of a full series element) and adds in shunt. a shuntannulling element consisting of .52, in series with 3.2362,. The othermethod terminates the network in BOO-shunt (that is. in a shunt elementwhose admittance is .809 times that of a full shunt element) and adds inseries. a series annulling element consisting of .3092, in shunt with22,. (See Figs. 6 to 11 inclusive). The theory underlying these im'pedance corrective designs is as follows:

It is well known that a smooth line having uniform series impedancedistributions .a,

has;

1 and a propagation constant A ware filter such as illustrated in Fig.6, having series element .2, and shunt element has a characteristicimpedance at any termination which is a function of both the productandratio of 2', and 2., and has a propagation constant which is a functionof their ratio. Hence it has been found convcnient to express both thecharacteristic impedance and propagation constant of the wave filter interms of k and f, the parameters of the corresponding smooth line. Aspointed out in the Campbell patent above referred to, free transmissionoccurs in such wave filters, (if infinitely long) for a range offrequencies corresponding to the range Let us now determine the:r-series characteristic admittance, A of a wave filter, having a serieselement a, and a shunt element per section. {eferring to the diagram ofFig. 2 the .e-serics impedance Z of such a lilter with an infinity ofrecurrent sections may be expressed as follows:

E2( n+ l) n't' z+ l This expression, by simple algebraic transformationmay be expressed j; Jaz 2 (I .5)2 (6) Multiplying both numerator anddenominator by we get 7 lies between 0 and 4, the admittance may beconsidered as being made up as two con'iponents, the conductance, C andthe susceptance, S This may be expressed as follows:

i xs i 1+ 1 1 and (.5x)'y 1 1+."c(1:c)'y -lr (11) Now it is apparentthat the susceptanc e may be annulled in equation 8 by a shunt annullingelement of equal value and opposite in sign to the value of thesusceptance given in equation 11. The admittance A of the shunt elementmust then be 1+x(1x)'y Since the impedance Z, of the anuulling elementis the reciprocal of the admittance,

1 or equation 12 may be rewritten by substituting the values of y and 70as follows From the form of this equation it is apparent that. the shuntannulling element consists 01" two parts in seriesone part having animpedance a; .5 and the other part having an impedance This only holdstrue when r is greater than .5 because if m is less than .5 thesequantities become negative and cannot be realized physically. Thecircuit arrangement of a filter terminating in rc-series. and having ashunt annulling element conforming to equation 13 is illustratedschematically in Fig. 3. In the arrangement of Fig. 3. if a is greaterthan .5 and the shunt annulling element is provided, there is left onlythe first part of the admittance of the filter, which, in thetransmitting range,-is the conductance C,,. The conductance coeflicientmay be written as follows:

equal to and the impedance to in --constant in the transmitting range.

We will now determine the proper impedance corrective design for afilter having an w-shunt termination. Such a filter is indicatedschematically in Fig. 4, and from this figure it is apparent that the:v-shunt impedance Z, may be written as follows:

The impedance Z of a filter having a full termination may, from Fig. 4,be expressed as follows:

z,Z 1+ m Substituting this value of Z in formula 15, we have, by simplealgebraic transformation Multiplying both numerator and denominifi atorby and simplifying, we have Substituting the values of equation becomes7 and k, this nae-1,2

nulled by a series element whose impedance is equal to the secondcomponent and opposite in sign. Thus (z.5)'y 1 +z(1 :r)'y' Substitutingthe values of Y and k in equation 20, we have, by simple algebraictransformation From equation 21 it is apparent that the annullingelement may consist of two parallel elements, whose impedances are (a:.5): and I a: .5 :c(1 -x) res tively where a: is greater than .5.

his arrangement is illustrated in Fig. 5, and when provided it isobvious that only the first part of the impedance of the filter remainsthis part in the transmitting range being the resistance R Theresistance coefficient T is the same coeflicient as given in equation14, and from Fig. 1 is nearly unity over the greater part of thetransmittin range, when a: has a value of about .8. once with atermination of .8 shunt the resistance R will, in the constant k typesof filters, be substantially equal to k in the transmitting range.

The network here disclosed in connection with Figures 4 and 5 servesequally well at the input end or the drop end of the filter, as may beshown by an explanation similar to that for Figs. 2 and 8.

Since, in practice, it is customary to terminate filters and other'formsof networks in mid-series or mid-shunt terminations instead of .8terminations, it is desirable that annulling elements be rovided formid-shunt and mid-series terminations. Fig. 6 illustrates a filterterminating in mid-series, and Figs. 7 and 8 illustrate the annullingelements to correspond thereto. These annulling elements are so designedas to be made up of a few simple standard elements, which may be used inthe construction of any type of corrective network to be used with wavefilters having either mid-series or mid-shunt characteristic impedancesequivalent to those of the constant k" type. In the design illustrateda: has been given a value of .809 which not onl has the advantage ofbeing near .8, whic as shown in Fig. 1 is the most desirable value, butalso permits of a similarity in the elements of both the shunt andseries annulling networks. This value of w is chosen because then InFig. 7 the shunt annulling element is made up of two elements havingvalues .52, and 3.2362 these values corresponding to those given byequation 13. In addition a series element having a value of .3092 isalso provided. This series element is simply employed so that it, whentaken with the midseries termination of .52, in Fig. 6, gives-in efl'ecta termination of 8092,.

In Fig. 8 the mid-series terminating filter of Fig. 6 is built out byadding a series element of .52 thus making a full series element for thesection, and the shunt element having the value 1.256s is provided,since this corresponds to a .809 shunt termination. This permits ofusing the elements of a series annulling element, such as is ordinarilyused with an w-shunt terminatin filter. These elements, as indicated,have t 1e values .3092, in parallel with 22 A comparison of Figs. 7 and8 shows that the two annulling devices are constructed from identicalunits.

Fig. 9 illustrates a filter terminating in mid-shunt while Figs. 10 and11 illustrate the corresponding annulling elements to be used therewith.In Fig. 10 the shunt element, having the value 32362,, when placed inarallel with the shunt termination of 22 in ig. 9, gives an effectiveshunt termination of The series annulling elements themselves are thesame as in Fig. 8, and have the values given by the formula 21. In Fig.11 the mid-shunt termination of Fig. 9 is built out to a full shuntsection by means of the shunt element 22 and the filter is given inefl'ect a .809 series termination by means of the series element 8092,.The shunt annulling elements then used are the same as those shown inFig. 7.

The principles employed in Figs. 6 to 11 inclusive, are shown applied toa low pass type of filter in Figs. 12 to 17 inclusive. The design of thenetworks of these figures will be apparent without further description.Similarly Figures 18 to 23 inclusive give the corresponding designs forhigh pass filters terminating either in mid-series or midshunt, andFigs. 2-1 to 29 inclusive, give the designs for single band filtersterminating either in mid-series or mid-shunt.

In all of these cases it will be seen that two alternative annullinnetworks are provided for each mid-serles and each midshunt termination,and that the elements of the second network of each pair will alwaysgive the elements of the first network of each air.

The annulling elements have an additional for. under thesecircumstances, the shunt anuulhng element Z becomes resonant, that is.

Also the series annulling Z, becomes antiresonant, that is or expressedin another way .309z, +22 :0. This result also follows from theperfectly general property of these annulling elements wherein, for thesame value of :0, their product 1S It will be obvious that the generalprinciples herein disclosed may be embodied in man other organizationswidely different from those illustrated without departing from thespirit of the invention, as defined in the following claims.

What I claim is: y

1. In a transmission circuit a wave filter comprising a plurality oflikesections, each section comprising series and shunt impedanceelements, at leastone of said elements including both inductance andcapacity, and a terminating network unlike said sections associated withsaid filter, said network being so proportioned as to neutralize thereactance component of the impedance of the filter over practically theentire range of free transmission and to equalize the correspondingresistance component to a constant value.

2. In a transmission circuit a. wavefilter comprising a plurality oflike sections, each section comprising series and shunt impedanceelements, at least one of said elements including both inductance andcapacity, and a terminating network unlike said sections associated withsaid filter, said network being so proportioned as to equalize thereactance component and the resistance component of the impedance of thefilter each to a constant value over practically the entire range offree transmission.

3. In a transmission circuit a wave filter comprising aplurality of likesections, each section comprising .series and shunt impedance elements,at least one of said elements including both inductance and capacity,and a terminating network unlike said sections associated with saidfilter, said network being so proportioned as to neutralize the revassociated with said filter, said network bemg so proportioned as toneutralize the susceptance component of the admittance of the filter,within its free transmitting range. 5. In a transmission circuit a wavefilter comprising a plurality of like sections, the end section of theseries being only a fractional part of the other sections, and aterminating network associated with said end section, said network beingso proportioned with respect to the filter as to neutralize thereactance component of the impedance of the filter over practically theentire range of free transmission and to equalize the correspondingresistance component to a constant value. I I 6. In a transmissioncircuit a wave filter comprising a plurality of like sections, the endsection of the series being only a fractional part of the othersections, and a transmitting network associated with said end section,said network being so proportioned that the reactance and resistancecomponents of the impedance of the filter over substantially the entirerange of free transmission will each be equalized respectively to aconstant value.

7. In a transmission circuit a wave filter comprising-a plurality oflike sections, the end section of the series being only a fractionalpart of the other sections, and a terminating network associated withsaid end section, said network being so pro ortioned that the reactancecomponent o the impedance will be neutralized over a substantial rangeof frequencies.

8. In a transmission circuit a wave filter comprising a plurality oflike: sections, the end section of the series being only a fractionalpart of the other sections, and a terminating network associatedwith-said end section, said network being so proportioned thatthe/susceptance component of the admittance will be substantiallyneutralized 0v r the range of freetransmission.

9. In a transmission circuit a wave filter comprising a plurality oflike sections, means to build outthe terminating section so that thefilter may be given either a fractional series or a fractional shunttermination, and an annulling network to be connected either in seriesor in shunt with the termination of the filter for neutralizing thereactance component of the impedance of the filter, the elements of thebuilding out means and the annulling network being so a terminatingnetwork applied to the last section of the wave filter, said networkcomrising means to present substantially an infinite impedance at afrequency just outside of the free range of transmission, thereby givingthe filtcr a very sharp cut-ofi'.

11. In a transmission system a wave filter comprising a plurality oflike sections, each section comprising series and shunt impedanoeelements, at least one of said elements including both inductance andcapacity, and a terminating network applied to .the last section of thewave filter, said network being so pro oitioned as to render theimpedance of t e wave filter substantially constant over the range offree transmission and comprising means to present practically aninfinite impedance to a frequency just outside the range of freetransmission, thereby giving the filter a sharp cutoff.

12. A wave filter having a fractional end section and a net involvingthe fractional value in its design, said net being so proportioned as toneutralize the reactance component of the impedance of the filter overthe free transmitting range, the said fractional end section being takenat such a fractional value that the combination gives the nearestapproximation to a constant resistance for the resistance component ofthe impedance thereof.

13. A wave filter having alternately disposed series impedances andshunt impedances, the product of the series impedance value by the shuntim dance value bein constant, said filter havin a fractional on sectionand a net involvin the fractional value in itsdesign, said net ing soproportioned as to neutralize the reactance component of the impedanceof the filter over the free transmitting range, the said fractional endsection being taken at such a fractional value that the combinationgives the nearest approximation to a constant resistance for theresistance component of the impedance thereof.

14. In combination, a wave filter and means to neutralize its reactancecomponent and -equalize its resistance compm nent to a substantiallyconstant value over the free transmitting range of the filter.

15. In combination, a wave filter 'and a terminal network to neutralizethe reactance component of the impedance within the free transmittingrange and to equalize the resistance component of the impedance with- 1in the free transmitting range.

16. In combination, a wave filter, a piece of apparatus of substantiallyconstant resistance connected thereto, and an interposed network toneutralize the reactance component of the impedance of the filter andapproximately equalize its resistance component to the resistance ofsaid piece of apparatus.

17. In combination, a wave filter having recurrent alternately disposedseries impedances a and shunt admittances l/a and at one end the serieselement of value X times one of the foregoing elements where X is a realnumber less than unity, and at the same end a network whose impedancevalue is a function of X and which is so proportioned as to neutralizethe reactance component of the impedance of the filter.

18. In combination, a wave filter having alternately disposed series.impedances 2 and shunt admittances l/z, and at one end a series elementwhich is 0.809 times one of the foregoing elements and in combination animpedance so proportioned as to neutralize the reactance component ofthe impedance of said filter.

19. A wave filter having a fractional end section, the value of thefraction being chosen most nearly to make the resistance componentconstant and also having a terminal network to neutralize the reactancecomnent corresponding to the value chosen or the said fraction.

20. A wave filter having alternately disposed series impedances andshunt admittances with a fractional element being a fraction of one ofthe foregoing at one end and in combination therewith a network toneutralize the reactance of the said filter.

In testimony whereof, I have signed my name to this specification this28th day of April 1920.

orro 'J. ZOBEL.

